The Outer Synchronization Between Two Complex Dynamical Networks With Stochastic Circumstance Noise

There are a variety of noise sources in the nature and industrial, such as lightning, high-powerelectrical equipment turned on or turned off and so on. The various forms of interference caused ofthese sources exist everywhere in our human society, and always affect our lives negatively. Due tothe difficult to predict the noise waveform exactly, so we turn it collectively referred to as therandom noise.Complex networks exist widely in our human society and the nature. In recent years, a great dealof research topics have focused on the dynamic problems of complex networks, among which,synchronization of all dynamical nodes in networks is having attracted many scholars’ attention andis becoming a new research focus. In this dissertation, based on Lyapunov stability theory, pinningcontrol and global control approaches, the synchronization problem of some complex dynamicalnetworks with stochastic circumstance noise is addressed.The main contents are as follows:Firstly, under the circumstance of stochastic noise, considering the state-coupling networks withtime delay, the outer synchronization between two complex dynamical networks is investigated. Torealize network synchronization and reduce control cost, the pinning controllers are only applied tosome significant nodes of the network. Several sufficient conditions are derived to synchronize twocomplex dynamical networks with pinning control. Then two numerical simulations are provided todemonstrate the effectiveness of the proposed pinning control.Secondly, under the circumstance of noisy transmission channel, considering the state-couplingcomplex dynamical networks with time delay and the output-coupling complex dynamical networkswith time delay, the outer synchronization between two nonidentical complex networks is studied.Considering the two different topology of the complex dynamic networks, some sufficientconditions of the outer synchronization between two nonidentical complex networks are derived.Then some examples are used to show the effectiveness of the designed controllers.Thirdly, based on the study of the outer synchronization between the two complex dynamicalnetworks in the above, the state estimation problem of the complex dynamical network withstochastic coupling under circumstance is further studied. According to the different coupling mode,the uncertainty of coupling in the nodes of the complex dynamical networks and the phenomenon of packet loss caused by the time delay are considered. In view of the stochastic state coupling andstochastic output coupling, some sufficient conditions are derived. Then some numericalsimulations are provided to show the effectiveness of the proposed state observers.